/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.jar /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.jar # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 96 ms] (2) JBC problem (3) JBCToGraph [EQUIVALENT, 342 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 0 ms] (6) JBCTerminationSCC (7) SCCToIRSProof [SOUND, 77 ms] (8) IRSwT (9) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 8 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT (15) TempFilterProof [SOUND, 39 ms] (16) IntTRS (17) RankingReductionPairProof [EQUIVALENT, 20 ms] (18) YES ---------------------------------------- (0) Obligation: need to prove termination of the following program: public class AProVERec01 { public static void main(String[] args){ List a = new List(args[0].length(), null); rec(args[1].length(), a); } public static void rec(int y, List res){ int x = 3 * y; if(x < 100000){ rec(x+1, res); } x = x*2; res.add(x); } } class List { int val = 0; List next = null; List (int v,List n){ val = v; next = n; } public void add(int newVal){ if (next == null) { next = new List(newVal, null); } else { next.add(newVal); } } } ---------------------------------------- (1) BareJBCToJBCProof (EQUIVALENT) initialized classpath ---------------------------------------- (2) Obligation: need to prove termination of the following program: public class AProVERec01 { public static void main(String[] args){ List a = new List(args[0].length(), null); rec(args[1].length(), a); } public static void rec(int y, List res){ int x = 3 * y; if(x < 100000){ rec(x+1, res); } x = x*2; res.add(x); } } class List { int val = 0; List next = null; List (int v,List n){ val = v; next = n; } public void add(int newVal){ if (next == null) { next = new List(newVal, null); } else { next.add(newVal); } } } ---------------------------------------- (3) JBCToGraph (EQUIVALENT) Constructed TerminationGraph. ---------------------------------------- (4) Obligation: Termination Graph based on JBC Program: AProVERec01.main([Ljava/lang/String;)V: Graph of 141 nodes with 0 SCCs. AProVERec01.rec(ILList;)V: Graph of 45 nodes with 0 SCCs. List.add(I)V: Graph of 28 nodes with 0 SCCs. ---------------------------------------- (5) TerminationGraphToSCCProof (SOUND) Splitted TerminationGraph to 1 SCCs. ---------------------------------------- (6) Obligation: SCC of termination graph based on JBC Program. SCC contains nodes from the following methods: AProVERec01.rec(ILList;)V SCC calls the following helper methods: AProVERec01.rec(ILList;)V, List.add(I)V Performed SCC analyses: *Used field analysis yielded the following read fields: *Marker field analysis yielded the following relations that could be markers: ---------------------------------------- (7) SCCToIRSProof (SOUND) Transformed FIGraph SCCs to intTRSs. Log: Generated rules. Obtained 17 IRulesP rules: f426_0_rec_Load(EOS(STATIC_426), i61, i61, matching1) -> f428_0_rec_IntArithmetic(EOS(STATIC_428), i61, 3, i61) :|: TRUE && matching1 = 3 f428_0_rec_IntArithmetic(EOS(STATIC_428), i61, matching1, i61) -> f431_0_rec_Store(EOS(STATIC_431), i61, 3 * i61) :|: TRUE && matching1 = 3 f431_0_rec_Store(EOS(STATIC_431), i61, i62) -> f433_0_rec_Load(EOS(STATIC_433), i61, i62) :|: TRUE f433_0_rec_Load(EOS(STATIC_433), i61, i62) -> f436_0_rec_ConstantStackPush(EOS(STATIC_436), i61, i62, i62) :|: TRUE f436_0_rec_ConstantStackPush(EOS(STATIC_436), i61, i62, i62) -> f438_0_rec_GE(EOS(STATIC_438), i61, i62, i62, 100000) :|: TRUE f438_0_rec_GE(EOS(STATIC_438), i61, i64, i64, matching1) -> f448_0_rec_GE(EOS(STATIC_448), i61, i64, i64, 100000) :|: TRUE && matching1 = 100000 f448_0_rec_GE(EOS(STATIC_448), i61, i64, i64, matching1) -> f455_0_rec_Load(EOS(STATIC_455), i61, i64) :|: i64 < 100000 && matching1 = 100000 f455_0_rec_Load(EOS(STATIC_455), i61, i64) -> f461_0_rec_ConstantStackPush(EOS(STATIC_461), i61, i64, i64) :|: TRUE f461_0_rec_ConstantStackPush(EOS(STATIC_461), i61, i64, i64) -> f463_0_rec_IntArithmetic(EOS(STATIC_463), i61, i64, i64, 1) :|: TRUE f463_0_rec_IntArithmetic(EOS(STATIC_463), i61, i64, i64, matching1) -> f465_0_rec_Load(EOS(STATIC_465), i61, i64, i64 + 1) :|: i64 >= 0 && matching1 = 1 f465_0_rec_Load(EOS(STATIC_465), i61, i64, i68) -> f467_0_rec_InvokeMethod(EOS(STATIC_467), i61, i64, i68) :|: TRUE f467_0_rec_InvokeMethod(EOS(STATIC_467), i61, i64, i68) -> f470_0_rec_ConstantStackPush(EOS(STATIC_470), i68, i68) :|: i68 >= 1 && i68 > i64 f467_0_rec_InvokeMethod(EOS(STATIC_467), i61, i64, i68) -> f470_1_rec_ConstantStackPush(EOS(STATIC_470), i61, i64, i68) :|: i68 >= 1 && i68 > i64 f470_0_rec_ConstantStackPush(EOS(STATIC_470), i68, i68) -> f472_0_rec_ConstantStackPush(EOS(STATIC_472), i68, i68) :|: TRUE f472_0_rec_ConstantStackPush(EOS(STATIC_472), i68, i68) -> f512_0_rec_ConstantStackPush(EOS(STATIC_512), i68, i68) :|: TRUE f512_0_rec_ConstantStackPush(EOS(STATIC_512), i68, i68) -> f424_0_rec_ConstantStackPush(EOS(STATIC_424), i68, i68) :|: TRUE f424_0_rec_ConstantStackPush(EOS(STATIC_424), i61, i61) -> f426_0_rec_Load(EOS(STATIC_426), i61, i61, 3) :|: TRUE Combined rules. Obtained 2 IRulesP rules: f426_0_rec_Load(EOS(STATIC_426), i61:0, i61:0, 3) -> f426_0_rec_Load(EOS(STATIC_426), 3 * i61:0 + 1, 3 * i61:0 + 1, 3) :|: 3 * i61:0 < 100000 && 3 * i61:0 >= 0 && 3 * i61:0 + 1 > 3 * i61:0 Removed following non-SCC rules: f426_0_rec_Load(EOS(STATIC_426), i61:0, i61:0, 3) -> f470_1_rec_ConstantStackPush(EOS(STATIC_470), i61:0, 3 * i61:0, 3 * i61:0 + 1) :|: 3 * i61:0 < 100000 && 3 * i61:0 >= 0 && 3 * i61:0 + 1 > 3 * i61:0 Filtered constant ground arguments: f426_0_rec_Load(x1, x2, x3, x4) -> f426_0_rec_Load(x2, x3) EOS(x1) -> EOS Filtered duplicate arguments: f426_0_rec_Load(x1, x2) -> f426_0_rec_Load(x2) Finished conversion. Obtained 1 rules.P rules: f426_0_rec_Load(i61:0) -> f426_0_rec_Load(3 * i61:0 + 1) :|: 3 * i61:0 >= 0 && 3 * i61:0 + 1 > 3 * i61:0 && 3 * i61:0 < 100000 ---------------------------------------- (8) Obligation: Rules: f426_0_rec_Load(i61:0) -> f426_0_rec_Load(3 * i61:0 + 1) :|: 3 * i61:0 >= 0 && 3 * i61:0 + 1 > 3 * i61:0 && 3 * i61:0 < 100000 ---------------------------------------- (9) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (10) Obligation: Rules: f426_0_rec_Load(i61:0) -> f426_0_rec_Load(arith) :|: 3 * i61:0 >= 0 && 3 * i61:0 + 1 > 3 * i61:0 && 3 * i61:0 < 100000 && arith = 3 * i61:0 + 1 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f426_0_rec_Load(i61:0) -> f426_0_rec_Load(arith) :|: 3 * i61:0 >= 0 && 3 * i61:0 + 1 > 3 * i61:0 && 3 * i61:0 < 100000 && arith = 3 * i61:0 + 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) f426_0_rec_Load(i61:0) -> f426_0_rec_Load(arith) :|: 3 * i61:0 >= 0 && 3 * i61:0 + 1 > 3 * i61:0 && 3 * i61:0 < 100000 && arith = 3 * i61:0 + 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: f426_0_rec_Load(i61:0:0) -> f426_0_rec_Load(3 * i61:0:0 + 1) :|: 3 * i61:0:0 >= 0 && 3 * i61:0:0 + 1 > 3 * i61:0:0 && 3 * i61:0:0 < 100000 ---------------------------------------- (15) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f426_0_rec_Load(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (16) Obligation: Rules: f426_0_rec_Load(i61:0:0) -> f426_0_rec_Load(c) :|: c = 3 * i61:0:0 + 1 && (3 * i61:0:0 >= 0 && 3 * i61:0:0 + 1 > 3 * i61:0:0 && 3 * i61:0:0 < 100000) ---------------------------------------- (17) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f426_0_rec_Load ] = -1*f426_0_rec_Load_1 The following rules are decreasing: f426_0_rec_Load(i61:0:0) -> f426_0_rec_Load(c) :|: c = 3 * i61:0:0 + 1 && (3 * i61:0:0 >= 0 && 3 * i61:0:0 + 1 > 3 * i61:0:0 && 3 * i61:0:0 < 100000) The following rules are bounded: f426_0_rec_Load(i61:0:0) -> f426_0_rec_Load(c) :|: c = 3 * i61:0:0 + 1 && (3 * i61:0:0 >= 0 && 3 * i61:0:0 + 1 > 3 * i61:0:0 && 3 * i61:0:0 < 100000) ---------------------------------------- (18) YES